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 Instructional Focus DocumentGrade 4 Mathematics
 TITLE : Unit 08: Measurement SUGGESTED DURATION : 14 days

Unit Overview

Introduction
This unit bundles student expectations that address solving problems dealing with perimeter and area, measurement units and conversions within the customary and metric systems, length, time, liquid volumes, mass, and money. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Grade 3, students determined the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row. They determined the perimeter of polygons or a missing length when given perimeter and remaining side lengths in problems. Students also used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories. Additionally, students determined solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools, and found liquid volume and weight using appropriate units and tools.

During this Unit
Students begin the formal introduction to formulas to determine the perimeter and area of rectangles and squares. Students use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w). In order to develop the formulas for perimeter and area, students identify parallel and perpendicular lines. Grade 4 is the first grade level where students are formally introduced to formulas as seen on the STAAR Grade 4 Mathematics Reference Materials. Students are expected to solve problems related to perimeter and area of rectangles where dimensions are whole numbers. In addition to solving problems involving length, students also solve problems that deal with measurements of intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, and/or division as appropriate. Students identify relative sizes of measurement units within the customary and metric systems and apply this knowledge to conversion of measurements within the same measurement system, customary or metric. Conversions are limited to one-step from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.

After this Unit
In Unit 09, students will continue to identify parallel and perpendicular lines as they examine geometric concepts that include points, lines, line segments, rays, and angles. In Grade 5, students will use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l × w × h, V = s × s × s, and V = Bh). They will represent and solve problems related to perimeter, area, and volume. Students will also solve problems by calculating conversions within a measurement system, customary or metric.

Research
According to authors Chapin and Johnson (2000), “In order to prepare elementary students to use measurement in a variety of ways, we must provide them with many opportunities to engage in meaningful measurement tasks-tasks that promote understanding of concepts and facility with measurement units” ( p. 195). The National Council of Teachers of Mathematics (2010) states that “One challenge for students is to understand the distinction between length and area. In fourth grade, students should have the opportunity to distinguish between the area and the perimeter of a shape and to realize that neither one determines the other” (p. 69).

Chapin, S & Johnson, A. (2000). Math matters: Understanding the math you teach. Sausalito, CA: Math Solutions Publications.
National Council of Teachers of Mathematics. (2010). Focus in grade 5: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life? Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life. Why is developing geometric, spatial, and measurement reasoning essential? How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Recognizing and understanding numerical patterns and relationships leads to efficient, accurate, and flexible representations (whole numbers).
• How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
• What patterns and relationships can be found within between the words, models, and formulas used to represent a geometric problem situation?
• How do models aid in visualizing and developing formulas for …
• perimeter of a rectangle?
• perimeter of a square?
• area of a rectangle?
• Why is it important to identify parallel or perpendicular lines within a figure before applying the formula for …
• perimeter of a rectangle?
• perimeter of a square?
• area of a rectangle?
• Why is it important to understand when and how to use formulas?
• What strategies can be used to determine the …
• perimeter of a rectangle?
• perimeter of a square?
• area of a rectangle?
• What relationships exist between …
• perimeter and area?
• addition and perimeter?
• multiplication and area?
• Attributes of objects and events can be measured using tools, and their measures can be described using units, in order to quantify a measurable attribute of the object or event.
• What units of measure are used to describe …
• customary length?
• metric length?
• perimeter?
• area?
• customary liquid volume (capacity)?
• metric liquid volume (capacity)?
• mass?
• time?
• What relationships exist between length and …
• perimeter?
• area?
• What relationships exist within and between different units of …
• customary length?
• metric length?
• customary liquid volume (capacity)?
• metric liquid volume (capacity)?
• mass?
• time?
• In what situations might someone need to convert from one measurement unit to another?
• What strategies can be used to convert from a …
• smaller unit to a larger unit?
• larger unit to a smaller unit?
• How does estimating the relative sizes of measurement units aid in solving measurement problems?
• What strategies can be used to solve problems involving …
• length?
• intervals of time?
• liquid volume?
• mass?
• money?
• How are descriptions of a length of time and descriptions of a time of day similar and different?
• How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
• Algebraic Reasoning
• Geometric Relationships
• Formulas
• Perimeter
• Area
• Representations
• Concrete models
• Pictorial models
• Expressions
• Equations
• Geometry
• Geometric Attributes and Properties
• Geometric Representations
• One-dimensional figures
• Two-dimensional figures
• Measurement
• Measureable Attributes
• Distance and length
• Capacity and liquid volume
• Mass
• Time
• Money
• Measure
• Systems of measurement
• Units of measure
• Conversions
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may use a formula to find area of a rectangle but misunderstand that area could also be found by arranging an array of unit squares that sufficiently cover that rectangle.
• Some students may confuse situations that require finding area with those that require finding perimeter.
• Some students have difficulty with the inverse relationship between the size of unit and the number of units measured and therefore apply the incorrect operation when converting from a smaller unit to larger unit or larger unit to smaller unit.
• Although some students may understand base-10 place value, they may overgeneralize its use to inappropriate situations, such as conversion of units of time.

Underdeveloped Concepts:

• Some students may begin measuring at the end of the ruler instead of at zero, while some students may begin measuring beginning with the number 1 on the ruler without compensating for the missing unit.
• When measuring with a ruler, some students might count the lines instead of the spaces.
• Some students may read the endpoint on a ruler as the answer to a measurement situation without fully understanding that length is the total distance from zero to the endpoint of the object being measured.

Unit Vocabulary

• Area – the measurement attribute that describes the number of square units a figure or region covers
• Conversion – a change from one measurement unit to another measurement unit without changing the amount
• Intersecting lines – lines that meet or cross at a point
• Length – the measurement attribute that describes a continuous distance from end to end
• Line – a set of points that form a straight path that goes in opposite directions without ending
• Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
• Mass – the measurement attribute that describes the amount of matter in an object (mass remains constant, regardless of location)
• Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Perpendicular lines – lines that intersect at right angles to each other to form square corners
• Relative size – size in relation to a measure
• Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object (weight depends upon location)

Related Vocabulary:

 Analog clock Angle corner Attribute Beaker Capacity Cent Centimeter Composite figure Congruent Cup Customary Day Decimeter Digital clock Dollar Duration Edge Elapsed time End time Eye dropper Fluid ounce Foot Formula Gallon Graduated cylinder Gram Hour Inch Interval Kilogram Kiloliter Kilometer Length Liter Measuring container or jar Measuring cup Measuring tape Meter Meter stick Metric Mile Milligram Milliliter Millimeter Minute Money Month Number line Ounce Pan balance Pint Polygon Pound Quart Rectangle Rule/process Ruler Scale Second Side Spring scale Square Start time Stop watch Ton Triple beam balance Unit Vertex Week Width Yard Yardstick
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Grade 4 Mathematics TEKS

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE Legend:

• Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
• Student Expectations (TEKS) identified by TEA are in bolded, black text.
• Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
• Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
• Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
• Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific clarifications are in italicized, blue text.
• Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
• A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
TEKS# SE# TEKS SPECIFICITY
4.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

• Mathematical problem situations within and between disciplines
• Everyday life
• Society
• Workplace

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• X. Connections
4.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Process Standard

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• VIII. Problem Solving and Reasoning
4.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS

Including, but not limited to:

• Appropriate selection of tool(s) and techniques to apply in order to solve problems
• Tools
• Real objects
• Manipulatives
• Paper and pencil
• Technology
• Techniques
• Mental math
• Estimation
• Number sense

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• VIII. Problem Solving and Reasoning
4.1D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Process Standard

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

• Mathematical ideas, reasoning, and their implications
• Multiple representations, as appropriate
• Symbols
• Diagrams
• Language

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• IX. Communication and Representation
4.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• IX. Communication and Representation
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
• Current knowledge to new learning

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• X. Connections
4.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

• Mathematical ideas and arguments
• Validation of conclusions
• Displays to make work visible to others
• Diagrams, visual aids, written work, etc.
• Explanations and justifications
• Precise mathematical language in written or oral communication

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• Measuring angles
• Understanding decimals and addition and subtraction of decimals
• Building foundations for addition and subtraction of fractions
• TxCCRS:
• IX. Communication and Representation
4.5 Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:
4.5C Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w).

Use

MODELS TO DETERMINE THE FORMULAS FOR THE PERIMETER OF A RECTANGLE (l + w + l + w OR 2l + 2w), INCLUDING THE SPECIAL FORM FOR PERIMETER OF A SQUARE (4s) AND THE AREA OF A RECTANGLE (l x w)

Including, but not limited to:

• Rectangle
• 4 sides
• 4 vertices
• Opposite sides congruent
• 2 pairs of parallel sides
• 4 pairs of perpendicular sides
• 4 right angles
• Square (a special type of rectangle)
• 4 sides
• 4 vertices
• All sides congruent
• 2 pairs of parallel sides
• 4 pairs of perpendicular sides
• 4 right angles
• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Perimeter is an additive one-dimensional linear measure
• Models to determine formulas for perimeter
• Rectangle (P = l + w + l + w or P = 2l + 2w)
• Square (P = 4s)
• Area – the measurement attribute that describes the number of square units a figure or region covers
• Area is a multiplicative two-dimensional square unit measure.
• Models to determine formulas for area
• Rectangle (A = l × w)
• Square (A = s × s)

Note(s):

• Grade 4 introduces use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w).
• Grade 5 will use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l × w × h, V = s × s × s, and V = Bh).
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IV.C. Measurement Reasoning – Measurement involving geometry and algebra
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
4.5D Solve problems related to perimeter and area of rectangles where dimensions are whole numbers.

Solve

PROBLEMS RELATED TO PERIMETER AND AREA OF RECTANGLES WHERE DIMENSIONS ARE WHOLE NUMBERS

Including, but not limited to:

• Rectangle
• 4 sides
• 4 vertices
• Opposite sides congruent
• 2 pairs of parallel sides
• 4 pairs of perpendicular sides
• 4 right angles
• Square (a special type of rectangle)
• 4 sides
• 4 vertices
• All sides congruent
• 2 pairs of parallel sides
• 4 pairs of perpendicular sides
• 4 right angles
• Perimeter – a linear measurement of the distance around the outer edge of a figure
• Perimeter is a one-dimensional linear measure.
• Whole number side lengths
• Recognition of perimeter embedded in mathematical and real-world problem situations
• Formulas for perimeter from STAAR Grade 4 Mathematics Reference Materials
• Square
• P = 4s, where s represents the side length of the square
• Rectangle
• P = l + w + l + w or P = 2l + 2w, where l represents the length of the rectangle and w represents the width of the rectangle
• Determine perimeter when given side lengths with or without models
• Determine perimeter by measuring to determine side lengths
• Ruler, STAAR Grade 4 Mathematics Reference Materials ruler, yardstick, meter stick, measuring tape, etc.
• Determine missing side length when given perimeter and remaining side length
• Perimeter of composite figures
• Area – the measurement attribute that describes the number of square units a figure or region covers
• Area is a two-dimensional square unit measure.
• Whole number side lengths
• Recognition of area embedded in mathematical and real-world problem situations
• Formulas for area from STAAR Grade 4 Mathematics Reference Materials
• Square
• A = s × s, where s represents the side length of the square
• Rectangle
• A = l × w, where l represents the length of the rectangle and w represents the width of the rectangle
• Determine area when given side lengths with and without models
• Determine area by measuring to determine side lengths
• Ruler, STAAR Grade 4 Mathematics Reference Materials ruler, yardstick, meter stick, measuring tape, etc.
• Determine missing side length when given area and remaining side length
• Area of composite figures
• Multiple ways to decompose a composite figure to determine perimeter and/or area

Note(s):

• Grade 4 introduces solving problems related to perimeter and area of rectangles where dimensions are whole numbers.
• Grade 5 will represent and solve problems related to perimeter and/or area and related to volume.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IV.A. Measurement Reasoning – Measurement involving physical and natural attributes
• IV.C. Measurement Reasoning – Measurement involving geometry and algebra
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
4.6 Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:
4.6A

Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.

Supporting Standard

Identify

PERPENDICULAR AND PARALLEL LINES

Including, but not limited to:

• Line – a set of points that form a straight path that goes in opposite directions without ending
• Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
• Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or off-set lengths
• Notation may be given using chevrons or arrows to represent parallel lines.
• If more than one set of parallel lines are present, the number of chevrons or arrows distinguishes the sets of parallel lines.
• Intersecting lines – lines that meet or cross at a point
• Various orientations including vertical, horizontal, diagonal, and intersecting lines of even, uneven, or off-set lengths
• Perpendicular lines – lines that intersect at right angles to each other to form square corners
• Various orientations including vertical, horizontal, diagonal, and perpendicular lines of even, uneven, or off-set lengths
• Notation is given as a box in the angle corner to represent a right angle (square corner).
• Lines in polygons

Note(s):

• Grade 3 used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Measuring angles
• Grade Level Connections (reinforces previous learning and/or provides development for future learning)
• TxCCRS:
• III.A. Geometric Reasoning – Figures and their properties
• IX. Communication and Representation
4.8 Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:
4.8A Identify relative sizes of measurement units within the customary and metric systems.
Supporting Standard

Identify

RELATIVE SIZES OF MEASUREMENT UNITS WITHIN THE CUSTOMARY AND METRIC SYSTEMS

Including, but not limited to:

• Relative size – size in relation to a measure
• Sizes within a single system of measurement (e.g., sizes within customary or sizes within metric systems)
• Typically used units of measure and their relative sizes in words and abbreviations
• Metric unit names are based on prefixes attached to base unit.
• Base units include meter for length, liter for volume and capacity, and gram for mass.
• Kilo: one thousand base units
• Deci: one-tenth of a base unit
• Centi: one-hundredth of a base unit
• Milli: one-thousandth of a base unit
• Length – the measurement attribute that describes a continuous distance from end to end
• Customary units typically used for length
• Inch (in.)
• 12 inches (in.) = 1 foot (ft)
• Foot (ft)
• 1 foot (ft) = 12 inches (in.)
• 3 feet (ft) = 1 yard (yd)
• Yard (yd)
• 1 yard (yd) = 3 feet (ft)
• 1,760 yards (yd) = 1 mile (mi)
• Mile (mi)
• 1 mile (mi) = 1,760 yards (yd)
• Measurement tools typically used for customary length
• Rulers, yardsticks, measuring tapes
• Relative size of customary units of length in real-world context
• Metric units typically used for length
• Millimeter (mm)
• 10 millimeters (mm) = 1 centimeter (cm)
• Centimeter (cm)
• 1 centimeter (cm) = 10 millimeters (mm)
• 100 centimeters (cm) = 1 meter (m)
• Decimeter (dm)
• 1 decimeter (dm) = 100 millimeters (mm)
• 1 decimeter (dm) = 10 centimeters (cm)
• Meter (m)
• 1 meter (m) = 100 centimeters (cm)
• 1,000 meters (m) = 1 kilometer (km)
• Kilometer (km)
• 1 kilometer (km) = 1,000 meters (m)
• Measurement tools typically used for metric length
• Rulers, meter sticks, measuring tapes
• Relative size of metric units of length in real-world context
• Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
• Customary units typically used for liquid volume (capacity)
• Fluid ounce (fl oz)
• 8 fluid ounces (fl oz) = 1 cup (c)
• Cup (c)
• 1 cup (c) = 8 fluid ounces (fl oz)
• 2 cups (c) = 1 pint (pt)
• Pint (pt)
• 1 pint (pt) = 2 cups (c)
• 2 pints (pt) = 1 quart (qt)
• Quart (qt)
• 1 quart (qt) = 2 pints (pt)
• 4 quarts (qt) = 1 gallon (gal)
• Gallon (gal)
• 1 gallon (gal) = 4 quarts (qt)
• Measurement tools typically used for customary liquid volume
• Measuring cups, measuring containers or jars
• Relative size of customary units of liquid volume (capacity) in real-world context
• Metric units typically used for liquid volume (capacity)
• Milliliter (mL)
• 1,000 milliliters (mL) = 1 liter (L)
• Liter (L)
• 1 liter (L) = 1,000 milliliters (mL)
• 1,000 liters (L) = 1 kiloliter (kL)
• Kiloliter (kL)
• 1 kiloliter (kL) = 1,000 liters (L)
• Measurement tools typically used for metric liquid volume
• Beakers, graduated cylinders, eye droppers, measuring containers or jars
• Relative size of metric units of liquid volume (capacity) in real-world context
• Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object (weight depends upon location)
• Customary units typically used for weight
• Ounce (oz)
• 16 ounces (oz) = 1 pound (lb)
• Pound (lb)
• 1 pound (lb) = 16 ounces (oz)
• 2,000 pounds (lb) = 1 ton (T)
• Ton (T)
• 1 ton (T) = 2,000 pounds (lb)
• Measurement tools typically used for weight
• Spring scales, kitchen scales, bathroom scales
• Relative size of customary units of weight in real-world context
• Mass – the measurement attribute that describes the amount of matter in an object (mass remains constant, regardless of location)
• Metric units typically used for mass
• Milligram (mg)
• 1,000 milligrams (mg) = 1 gram (g)
• Gram (g)
• 1 gram (g) = 1,000 milligrams (mg)
• 1,000 grams (g) = 1 kilogram (kg)
• Kilogram (kg)
• 1 kilogram (kg) = 1,000 grams (g)
• Measurement tools typically used for mass
• Pan balances, triple beam balances
• Relative size of metric units of mass in real-world context
• Recognition of appropriate unit of measure in real-world context

Note(s):

• Grade 4 introduces identifying relative sizes of measurement units within the customary and metric systems.
• Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• TxCCRS:
• IX. Communication and Representation
4.8B Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
Supporting Standard

Convert

MEASUREMENTS WITHIN THE SAME MEASUREMENT SYSTEM, CUSTOMARY OR METRIC, FROM A SMALLER UNIT INTO A LARGER UNIT OR A LARGER UNIT INTO A SMALLER UNIT WHEN GIVEN OTHER EQUIVALENT MEASURES REPRESENTED IN A TABLE

Including, but not limited to:

• Whole numbers (0 – 1,000,000,000)
• Products of two-digit factors by two-digit factors and up to four-digit factors by one-digit factors
• Quotients up to four-digit dividends by one-digit divisors
• Decimals (less than one or greater than one)
• Limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
• Determined by reasoning that half of any value is that value divided by 2
• Fractions (proper, improper, and mixed numbers
• Limited to multiples of halves (e.g., etc.)
• Determined by reasoning that half of any value is that value divided by 2
• One-step conversions from a smaller unit to a larger unit or from a larger unit to a smaller unit
• Conversion – a change from one measurement unit to another measurement unit without changing the amount
• Typically used units of measure
• Customary
• Length: miles, yards, feet, inches
• Volume (liquid volume) and capacity: gallons, quarts, pints, cups, fluid ounces
• Weight: tons, pounds, ounces
• Metric
• Length: kilometer, meter, centimeters, millimeters
• Volume (liquid volume) and capacity: kiloliter, liter, milliliter
• Mass: kilogram, gram, milligram
• Based on prefixes attached to base unit
• Base units include meter for length, liter for volume and capacity, and gram for weight and mass.
• Kilo: one thousand base units
• Deci: one-tenth of a base unit
• Centi: one-hundredth of a base unit
• Milli: one-thousandth of a base unit
• Relationship between converting units
• Converting within the same measurement system, customary or metric
• Multiplication converts larger units to smaller units.
• Division converts smaller units to larger units.
• Convert measurements within the customary measurement system from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
• Length
• Rule/process column given in a table
• Rule/process column not given in a table
• Volume (liquid volume) and capacity
• Rule/process column given in a table
• Rule/process column not given in a table
• Weight
• Rule/process column given in a table
• Rule/process column not given in a table
• Convert measurements within the metric measurement system from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
• Length
• Rule/process column given in a table
• Rule/process column not given in a table
• Volume (liquid volume) and capacity
• Rule/process column given in a table
• Rule/process column not given in a table
• Mass
• Rule/process column given in a table
• Rule/process column not given in a table
• Equivalent measures in tables may have missing information in one or both columns.

Note(s):

• Grade 4 introduces converting measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
• Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• TxCCRS:
• I. Numeric Reasoning
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
4.8C Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

Solve

PROBLEMS THAT DEAL WITH MEASUREMENTS OF LENGTH, INTERVALS OF TIME, LIQUID VOLUMES, MASS, AND MONEY USING ADDITION, SUBTRACTION, MULTIPLICATION, OR DIVISION AS APPROPRIATE

Including, but not limited to:

• Whole numbers (0 – 1,000,000,000)
• Products of two-digit factors by two-digit factors and up to four-digit factors by one-digit factors
• Quotients up to four-digit dividends by one-digit divisors
• Decimals (greater than one and less than one)
• Addition and subtraction of money amounts up to hundredths
• Conversions limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
• Determined using reasoning that half of any value is that value divided by 2
• Fractions (proper, improper, and mixed numbers)
• Addition and subtraction of fractions with like denominators
• Conversions limited to multiples of halves (e.g., etc.)
• Determined using reasoning that half of any value is that value divided by 2
• Typically used customary and metric units
• Customary
• Length: miles, yards, feet, inches
• Volume (liquid volume) and capacity: gallons, quarts, pints, cups, fluid ounces
• Weight: tons, pounds, ounces
• Metric
• Length: kilometer, meter, centimeters, millimeters
• Volume (liquid volume) and capacity: kiloliter, liter, milliliter
• Mass: kilogram, gram, milligram
• Based on prefixes attached to base unit
• Base units include meter for length, liter for volume and capacity, and gram for weight and mass.
• Kilo: one thousand base units
• Deci: one-tenth of a base unit
• Centi: one-hundredth of a base unit
• Milli: one-thousandth of a base unit
• Typically used measurement tools
• Customary
• Length: rulers, yardsticks, measuring tapes
• Volume (liquid volume) and capacity: measuring cups, measuring containers or jars
• Metric
• Length: rulers, meter sticks, measuring tapes
• Volume (liquid volume) and capacity: beakers, graduated cylinders, eye droppers, measuring containers or jars
• Mass: pan balances, triple beam balances
• Problem situations that deal with measurements of length
• Addition, subtraction, multiplication, and/or division of measurements of length with or without conversion
• May or may not include using measuring tools to determine length
• Problem situations that deal with intervals of time (clocks: hours, minutes, seconds)
• Addition and subtraction of time intervals in minutes
• Such as a 1 hour and 45-minute event minus a 20-minute event equals 1 hour 25 minutes
• Time intervals given
• Pictorial models and tools
• Measurement conversion tables
• Analog clock with gears, digital clock, stop watch, number line, etc.
• Time conversions
• 1 hour = 60 minutes; 1 minute = 60 seconds
• Fractional values of time limited to multiples of halves
• Elapsed time
• Finding the end time
• Finding the start time
• Finding the duration
• Problem situations that deal with intervals of time (calendar: years, months, weeks, days)
• Time conversions
• 1 year = 12 months; 1 year = 52 weeks; 1 week = 7 days; 1 day = 24 hours
• Fractional values of time limited to multiples of halves
• Problem situations that deal with measurements of volume (liquid volume) and capacity
• Addition, subtraction, multiplication, and/or division of measurements of volume (liquid volume) and capacity with or without conversion
• May or may not include using measuring tools to determine volume (liquid volume) and capacity
• Problem situations that deal with measurements of mass
• Addition, subtraction, multiplication, and/or division of measurements of mass with or without conversion
• May or may not include using measuring tools to determine mass
• Problem situations that deal with money
• Addition and subtraction may include whole number or decimal amounts
• Multiplication and division limited to amounts expressed as cents or dollars with no decimal values
• Comparison of money amounts
• Making change
• Range of dollar amounts

Note(s):

• Grade 3 determined solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes.
• Grade 4 introduces solving problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
• Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
• TxCCRS:
• I. Numeric Reasoning
• VIII. Problem Solving and Reasoning
• IX. Communication and Representation
• X. Connections 